It is shown in [1]} that when \(\mathbf {A}\)  is a right-orthogonally invariant random matrix and sufficiently large, the per-iteration behavior of the denoiser and the LMMSE estimator in VAMP can be exactly predicted by a scalar state evolution. The right-orthogonally invariant matrix \(\mathbf {A}\)  allows arbitrary singular values and arbitrary left singular vectors, making VAMP robust against the distribution of \(\mathbf {A}\) . However, there are still two problems when it is used for massive device detection. First, the conventional VAMP algorithm assumes that the distribution parameters are known and assumes that the device state matrix is a Bernoulli-Gaussian distributed random matrix. However, in practical massive MIMO systems [2]}-[3]}, the device state matrix is a Bernoulli-Gaussian mixture distributed random matrix. As a result, the denoiser of the VAMP algorithm is not specifically designed for the massive device detection under investigation. Second, AWGN precision in \(\mathbf {u}_{1,r}\)  is not equal to \(\gamma  _{1}\)  when the distribution parameters are not perfect, which may lead to severe performance loss in VAMP algorithm.
